Pentagon (EntityTopic, 12)

From Hi.gher. Space

The pentagon can be seen as the two-dimensional analog to the dodecahedron in 3D and the cosmochoron in 4D. It is also the lowest-dimensional member of the ursatopes, with a (trivial) digonal base.


The coordinates of a regular pentagon centered at the origi and having side length 2 are:

(√((10+2√5)/5), 0)
(√((5-√5)/10), ±φ)
√((5+2√5)/5), ±1)

Where φ is the golden ratio (1+√5)/2.


  • The hypervolumes of a pentagon with side length l are given by:
total edge length = 5l
area = 14 · √(25+10√5) · l2

Incidence matrix

Dual: Self-dual

0 Va= point ;
1 Ea2= digon ;
2 5a55= pentagon ;

Usage as facets

Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle